One-Dimensional Consolidation of Unsaturated Soil Deposit with Various Initial Conditions

摘要

This study presents a novel analytical solution for one-dimensional (1-D) consolidation for unsaturated soils using the Eigen function expansion method to solve inhomogeneous governing equations of air and water phases. Eigen functions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary condition. Additionally, the Laplace transform method is adopted to solve the first-order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. The mathematical procedure accentuates a non-uniform initial condition, in which initial excess pore pressures are linearly decreasing with depth. Dimensionless parameters λ_a and λ_w that control the gradients of distributions of initial excess pore-air and pore-water pressures, respectively, are introduced in this paper. A worked example is provided to investigate effects of λ_a and λ_w on the consolidation behaviour of unsaturated soils.